Solve for $x$, ignoring any extraneous solutions: $\dfrac{x^2 - 9x}{x - 2} = \dfrac{8x - 70}{x - 2}$
Explanation: Multiply both sides by $x - 2$ $ \dfrac{x^2 - 9x}{x - 2} (x - 2) = \dfrac{8x - 70}{x - 2} (x - 2)$ $ x^2 - 9x = 8x - 70$ Subtract $8x - 70$ from both sides: $ x^2 - 9x - (8x - 70) = 8x - 70 - (8x - 70)$ $ x^2 - 9x - 8x + 70 = 0$ $ x^2 - 17x + 70 = 0$ Factor the expression: $ (x - 7)(x - 10) = 0$ Therefore $x = 7$ or $x = 10$